Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#18011934 | C2 | semidirect |
| 2. #23750297 | C2 | semidirect |
| 3. #23750278 | C2 | semidirect |
| 4. #23749999 | C2 | semidirect |
| 5. #23749857 | C2 | semidirect |
| 6. #23749821 | C2 | semidirect |
| 7. #23749786 | C2 | semidirect |
| 8. #23749773 | C2 | semidirect |
| 9. C4×#14558723 | C2 | semidirect |
| 10. #23749690 | C2 | semidirect |
| 11. #462×C149 | C2 | semidirect |
| 60. #14558723 | D4 | semidirect |
| 129. C4×C149 | #135 | semidirect |
| 140. C149 | #3284 | semidirect |
| 147. #462 | D149 | semidirect |
| 272. C4 | #18011934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011934 | 2 |
| #23750297 | 2 |
| #23750278 | 2 |
| #23749999 | 2 |
| #23749857 | 2 |
| #23749821 | 2 |
| #23749786 | 2 |
| #23749773 | 2 |
| C4×#14558723 | 2 |
| #23749690 | 2 |
| #462×C149 | 2 |
| #3284 | 149 |